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Melting of iron and other metals at earth’s core conditions: A simplified computational approach

Physical Review B 2001年第1期65卷 014104-014104页

作者： Y. Wang R. Ahuja B. Johansson Condensed Matter Theory Group Department of Physics Uppsala University Box 530 S-751 21 Uppsala Sweden Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 People’s Republic of China Applied Materials Physics Department of Materials Science and Engineering Royal Institute of Technology S-100 44 Stockholm Sweden

In order to study melting of metals at high pressure, we propose a different method which can be thought of as a generalization of the well-known Lindemann law. One essential interesting feature is that neither the Debye temperature nor the Grüneisen coefficient are used in the theory. We find that the method based on first-principles calculations can be used to model the pressure dependence of the melting properties of metals very well. Predictions of the melting along the principal Hugoniot are calculated for Cu and Ta. In the case of Fe, the melting temperature is calculated at geophysically interesting pressures.

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Physical Confinement and Cell Proximity Increase Cell Migration Rates and Invasiveness: A Mathematical Model of Cancer Cell Invasion Through Flexible Channels

SSRN

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SSRN 2022年

作者： Peng, Qiyao Vermolen, Fred J. Weihs, Daphne Mathematical Institute Faculty of Science Leiden University Neils Bohrweg 1 Leiden2333 CA Netherlands Computational Mathematics Group Department of Mathematics and Statistics Faculty of Science Hasselt University Campus Diepenbeek Agoralaan Gebouw D Diepenbeek3950 BE Belgium Delft Institute of Applied Mathematics Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands Faculty of Biomedical Engineering Technion-Israel Institute of Technology Haifa3200003 Israel

Cancer cell migration between different body parts is the driving force behind cancer metastasis, which is the main cause of mortality of patients. Migration of cancer cells often proceeds by penetration through narrow cavities in locally stiff, yet flexible tissues. In our previous work, we developed a model for cell geometry evolution during invasion, which we extend here to investigate whether leader and follower (cancer) cells that only interact mechanically can benefit from sequential transmigration through narrow micro-channels and cavities. We consider two cases of cells sequentially migrating through a flexible channel: leader and follower cells being closely adjacent or distant. Using Wilcoxon's signed-rank test on the data collected from Monte Carlo simulations, we conclude that the modelled transmigration speed for the follower cell is significantly larger than for the leader cell when cells are distant, i.e. follower cells transmigrate after the leader has completed the crossing. Furthermore, it appears that there exists an optimum with respect to the width of the channel such that cell moves fastest. On the other hand, in the case of closely adjacent cells, effectively performing collective migration, the leader cell moves $12\%$ faster since the follower cell pushes it. This work shows that mechanical interactions between cells can increase the net transmigration speed of cancer cells, resulting in increased invasiveness. In other words, interaction between cancer cells can accelerate metastatic invasion. © 2022, The Authors. All rights reserved.

关键词： Cells

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Dynamical Heterogeneities in a Supercooled Lennard-Jones Liquid

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Physical Review Letters 1997年第15期79卷 2827-2827页

作者： Walter Kob Claudio Donati Steven J. Plimpton Peter H. Poole Sharon C. Glotzer Institut für Physik Johannes Gutenberg-Universität Staudinger Weg 7 D-55099 Mainz Germany Center for Theoretical and Computational Materials Science and Polymers Division National Institute of Standards and Technology Gaithersburg Maryland 20899 Parallel Computational Sciences Department Sandia National Laboratory Albuquerque New Mexico 87185-1111 Department of Applied Mathematics University of Western Ontario London Ontario Canada N6A 5B7

We present the results of a molecular dynamics computer simulation study in which we investigate whether a supercooled Lennard-Jones liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian parameter for the self part of the van Hove correlation function and use it to identify “mobile” particles. We find that these particles form clusters whose sizes grow with decreasing temperature. We also find that the relaxation time of the mobile particles is significantly shorter than that of the average particle, and that this difference increases with decreasing temperature.

关键词： .Supercooled Lennard-Jones correlation function cantly Dynamical heterogeneities mobile particles increases with decreasing

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Ratio of forbidden transition rates in the ground-state configuration of O ii

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Physical Review A 2012年第6期85卷 062506-062506页

作者： Xiao-Ying Han Xiang Gao De-Ling Zeng Jun Yan Jia-Ming Li Data Center for High Energy Density Materials Institute of Applied Physics and Computational Mathematics Beijing 100088 China Beijing Computational Science Research Center Beijing 100084 China Institute of Atomic and Molecular Physics Jilin University Changchun 130012 China Key Laboratory for Laser Plasma (Ministry of Education) and Department of Physics Shanghai Jiao Tong University Shanghai 200240 China Department of Physics and Center for Atomic and Molecular Nanosciences Tsinghua University Beijing 100084 China

Based on a set of “quasicomplete bases,” using the large-scale multiconfiguration Dirac-Fock (MCDF) method, we calculate the forbidden electric quadrupole (E2) and magnetic dipole (M1) transition rates of the transitions 2D5/2,3/2o→4S3/2o of the O ii ground state considering the quantum electrodynamics (QED) corrections. Our calculations demonstrate that the Breit interactions are most important among all the QED corrections. The calculated E2 and M1 transition rates converge in a systematical and uniform manner with the extending orbital basis and the calculation uncertainty of 2.5% is achieved by considering the valence- and core-excitation correlations totally. With the converged transition rates, a value of the intensity ratio between the two transitions in high-electron-density limit in planetary nebulas is given, that is, r(∞)=0.363±0.009, which is within the overlap of the different observations and with the least uncertainty up to now. In addition, the E2 and M1 transition rates of two transitions 2P3/2,1/2o→4S3/2o of O ii ground state and the ratio between the two transition rates in high-electron-density limit are calculated and compared with the previous results.

关键词： Ground state

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Correlation and relativistic effects in U metal and U-Zr alloy: Validation of ab initio approaches

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Physical Review B 2013年第23期88卷 235128-235128页

作者： Wei Xie (谢玮) Wei Xiong Chris A. Marianetti Dane Morgan Materials Science Program University of Wisconsin-Madison Madison Wisconsin 53706 USA Department of Materials Science and Engineering University of Wisconsin-Madison Madison Wisconsin 53706 USA Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 USA Department of Engineering Physics University of Wisconsin-Madison Madison Wisconsin 53706 USA

Ab initio calculations have been performed on all solid phases of U metal and U-Zr alloy, the basis of a promising metallic fuel for fast nuclear reactors. Based on generalized gradient approximation, both density functional theory (DFT) in its standard form and the so-called DFT plus Hubbard U (DFT+U) modification are evaluated. The evolution of calculated energetics, volume, magnetic moments, electronic structure, and f-orbital occupation as functions of the effective Hubbard U parameter, Ueff, is carefully examined at Ueff from 0 to 4 eV. DFT is found to overestimate energetics, underestimate volume, downward shift some f bands near Fermi level and overestimate f-orbital occupation against existing experimental and/or computational data. The error is ∼0.07 eV/atom in terms of enthalpy, which affects phase stability modeling for δ(U,Zr) and γ(U,Zr). DFT+U at Ueff=1−1.5 eV offers clear improvement on these calculated properties (∼0.05 eV/atom in terms of enthalpy) and in general still neither promotes ordered magnetic moments nor opens unphysical band gaps, which occur at higher Ueff values. The empirical Ueff values of 1–1.5 eV are close to but smaller than the theoretical estimations of 1.9–2.3 eV that we obtain from the linear response approach. Ueff is found to vary only slightly (≤0.24 eV) between different phases and at different compositions of U and U-Zr; thus, a single Ueff=1.24 eV, which is the statistical optimal from energetic fitting, is suggested for both U and U-Zr. Besides correlation, the relativistic effect of spin-orbit coupling (SOC) is also systematically explored. SOC is found to lower energy, increase volume, and split the 5f shell above Fermi level and reduce f-orbital occupation. The effect predominates in the unoccupied states and is very small on all these calculated ground state properties (∼0.02 eV/atom in terms of enthalpy).

关键词： NUCLEAR reactors HUBBARD model ELECTRONIC structure FERMI level MAGNETIC moments

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Stochastic Approximation hamiltonian monte carlo

arXiv

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arXiv 2018年

作者： Jin, Ick Hoon Shin, Minsuk Liang, Faming Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Harvard Data Science Initiative Department of Statistics Harvard University CambridgeMA02138 United States Department of Statistics Purdue University West LafayetteIN47907 United States

Recently, the Hamilton Monte Carlo (HMC) has become widespread as one of the more reliable approaches to efficient sample generation processes. However, HMC is difficult to sample in a multimodal posterior distribution because the HMC chain cannot cross energy barrier between modes due to the energy conservation property. In this paper, we propose a Stochastic Approximate Hamilton Monte Carlo (SAHMC) algorithm for generating samples from multimodal density under the HMC framework. SAHMC can adaptively lower the energy barrier to move the Hamiltonian trajectory more frequently and more easily between modes. The convergence of the algorithm is established under mild conditions. Gaussian mixture model and neural network model show that SAHMC is superior to HMC when target posterior density has multiple modes. Copyright © 2018, The Authors. All rights reserved.

关键词： Monte Carlo methods

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A linked data graph approach to integration of immunological data

A linked data graph approach to integration of immunological...

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IEEE International Conference on Bioinformatics and Biomedicine

作者： Syed Ahmad Chan Bukhari Jeff Mandell Steven H. Kleinstein Kei-Hoi Cheung Division of Computer Science Mathematics and Science Lesley H. & William L. Collins College of Professional Studies St. John's University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Pathology Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Emergency Medicine and Yale Center for Medical Informatics Computationa Biology and Bioinformaticcs Yale University

ISBN: (纸本)9781728118680

Systems biology involves the integration of multiple data types (across different data sources) to offer a more complete picture of the biological system being studied. While many existing biological databases are implemented using the traditional SQL (Structured Query Language) database technology, NoSQL database technologies have been explored as a more relationship-based, flexible and scalable method of data integration. In this paper, we describe how to use the Neo4J graph database to integrate a variety of types of data sets in the context of systems vaccinology. Specifically, we have converted into a common graph model diverse types of vaccine response measurement data from the NIH/NIAID ImmPort data repository, pathway data from Reactome, influenza virus strains from WHO, and taxonomic data from NCBI Taxon. While Neo4J provides a graph-based query language (Cypher) for data retrieval, we develop a web-based dashboard for users to easily browse and visualize data without the need to learn Cypher. In addition, we have prototyped a natural language query interface for users to interact with our system. In conclusion, we demonstrate the feasibility of using a graph-based database for storing and querying immunological data with complex biological relationships. Querying a graph database through such relationships has the potential to reveal novel relationships among heterogeneous biological data.

关键词： ontology knowledgebase graph database immunology influenza vaccine graphic library Knowledge Bases Influenza Vaccines Ontology Immunology data integration Passwords DNA Integration integration data types Data sources SQL

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Microstructural degeneracy associated with a two-point correlation function and its information content

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Physical Review E 2012年第5期85卷 051140-051140页

作者： C. J. Gommes Y. Jiao S. Torquato Department of Chemical Engineering University of Liège Liège 4000 Belgium Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. In an earlier Letter [Gommes, Jiao, and Torquato, Phys. Rev. Lett. 108, 080601 (2012)], we addressed the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation of the methodology and analyses, as well as additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures, including realizations of hard disks and Poisson point processes at various densities as well as those with known degeneracies (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the

关键词： MICROSTRUCTURE CORRELATION (Statistics) INFORMATION theory ENTROPY (Information theory) GROUND state (Quantum mechanics) MONTE Carlo method POISSON processes

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Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling

Symplectic time-domain finite element method (STD-FEM) exten...

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2023 International Conference for Acoustic and vibration Engineers, NVHH 2023

作者： Huszty, Csaba Firtha, Gergely Izsák, Ferenc ENTEL Engineering Research & Consulting Ltd. Szépvölgyi út 32. BudapestH-1025 Hungary Department of Networked Systems and Services Faculty of Electric Engineering Budapest University of Technology and Economics Muegyetem rkp. 3. BudapestH-1111 Hungary Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Pázmány P. stny. 1.C BudapestH-1117 Hungary

The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity. © Published under licence by IOP Publishing Ltd.

关键词： Acoustic fields

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Spectral Top-Down Recovery of Latent Tree Models

arXiv

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arXiv 2021年

作者： Aizenbud, Yariv Jaffe, Ariel Wang, Meng Hu, Amber Amsel, Noah Nadler, Boaz Chang, Joseph T. Kluger, Yuval Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Computer Science Weizmann Institute of Science Rehovot76100 Israel Department of Statistics Yale University New HavenCT06520 United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University New HavenCT06511 United States Department of Pathology Yale University New HavenCT06511 United States

Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, recover the structure separately of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy. Copyright © 2021, The Authors. All rights reserved.

关键词： Recovery

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